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ABSTRACT
On the grounds of Kolmogorov's 4/5 law analytical relations for triple two-point correlations of velocity and velocity gradients in homogeneous isotropic incompressible turbulence are derived. The corresponding correlation tensor can be expressed in terms of dissipation ε, the second-order longitudinal velocity structure function and one more scalar function
of distance between the points. However, some components of the tensor do not depend on
. The derived analytical results are in agreement with the data obtained from direct numerical simulations. The function
can be well approximated in the inertial range by a constant value that depends on the dissipation ε only. The application of the obtained correlators in the turbulent transport theory is discussed.
Acknowledgments
The authors are thankful to A. S. Il'yn, V. A. Sirota, S. A. Chernyshev, and A. M. Kiselev for many fruitful discussions. We are also much obliged to A. M. Kiselev for providing the computation programs written by himself. These programs symbolically collapse the tensor indexes and solve linear systems of equations. Therefore, this allowed us to verify and deepen our analysis of the first order of the expansion and to calculate the second order of the expansion.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1 A.S. Il'yn, Private communication
2 Note that some of the relations (Equation17(17) ) can be deduced from (Equation3
(3) ) and (Equation12
(12) ) only. For instance, in the inertial interval they lead immediately to
and
.
5 These suggestions should be also checked in other numerical and experimental investigations.